Qualitative behaviour of a family of delay-differential models of the glucose-insulin system

By P. Palumbo, S. Panunzi, Andrea De Gaetano. 2006

123 citations recorded by the source corpus.

A family of delay-differential models of the glucose-insulin system is introduced, whose members represent adequately the Intra-Venous Glucose Tolerance Test and allied experimental procedures of diabetological interest. All the models in the family admit positive bounded unique solutions for any positive initial condition and are persistent. The models agree with the physics underlying the experiments, and they all present a unique positive equilibrium point.    Local stability is investigated in a pair of interesting member models: one, a discrete-delays differential system; the other, a distributed-delay system reducing to an ordinary differential system evolving on a suitably defined extended state space. In both cases conditions are given on the physical parameters in order to ensure the local asymptotic stability of the equilibrium point. These conditions are always satisfied, given the actual parameter estimates obtained experimentally. A study of the global stability properties is performed, but while from simulations it could be conjectured that the models considered are globally asymptotically stable, sufficient stability criteria, formally derived, are not actually satisfied for physiological parameters values. Given the practical importance of the models studied, further analytical work may be of interest to conclusively characterize their behavior.

Subfields: Endocrinology, Diabetes and Metabolism, Molecular Biology, Surgery

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In Endocrinology, Diabetes and Metabolism

1. Shamim Nemati
2. Chao Yu
3. Jiming Liu

In Molecular Biology

1. Shamim Nemati
2. Chao Yu
3. Jiming Liu

In Surgery

1. Shamim Nemati
2. Chao Yu
3. Jiming Liu

Citations in the corpus

• Reinforcement Learning in Healthcare: A Survey (2019, methodology): “Based on the Palumbo mathematical model [121], the onpolicy SARSA was used for insulin delivery rate [122].”